libirt.h File Reference

The exported functions definition of the libirt library. More...

#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>

Macros
#define	LIBIRT_H   1
	Define a flag if this header file is already included.
#define	BLANK   -1
	Define the representation of blank as integer.
#define	FALSE   0
	Define the representation of false as integer.
#define	TRUE   1
	Define the representation of true as integer.
#define	VERY_SMALL_PROB   ((double)1.0e-10)
	Define the smallest probability allowed.
#define	VERY_SMALL_FREQ   ((double)1.0e-3)
	Define the smallest frequency allowed.
#define	VERY_BIG_LOGIT   ((double)23.0)
	Define the biggest logit allowed in absolute value.
#define	MAX_POLYCOR   ((double)0.9999)
	Define the biggest absolute polyserial correlation allowed.

Functions
int	read_bin_patterns_delimited (FILE *file, int nbr_item, int nbr_subject, int skip, char delimiter, int offset, int extra, char *true_string, char *false_string, char *blank_string, int trimming, gsl_matrix_int **patterns)
	Read binary patterns from a file in delimited format.
int	read_mc_patterns_delimited (FILE *file, int nbr_item, int nbr_subject, int skip, char delimiter, int offset, int extra, int trimming, gsl_matrix_int **patterns, gsl_vector_int **nbr_options)
	Read multiple choice patterns from a file in delimited format.
double	logit (double p)
	Compute the logit transformation.
double	logistic (double t)
	Compute the logistic transformation.
double	prob_3plm (double ability, double slope, double threshold, double asymptote)
	Compute the 3 parameter logistic function.
void	quadrature (int nbr_quad, double from, double to, gsl_vector *quad_points, gsl_vector *quad_weights)
	Generate the quadrature classes.
void	patterns_counts (gsl_matrix_int *subjects, gsl_vector_int **index, gsl_matrix_int **patterns, gsl_vector **counts)
	Group the identical patterns from subjects into patterns.
void	probs_3plm (gsl_vector *slopes, gsl_vector *thresholds, gsl_vector *asymptotes, gsl_vector *quad_points, gsl_matrix *probs)
	Compute the response functions for a 3PLM.
void	likelihood (gsl_matrix_int *patterns, gsl_matrix *probs, gsl_matrix *like)
	Compute the likelihood of each patterns.
void	likelihood_mc (gsl_matrix_int *patterns, gsl_matrix *probs, gsl_vector_int *nbr_options, gsl_vector_int *items_pos, gsl_matrix *like)
	Compute the likelihood of each multiple choice patterns.
void	posteriors (gsl_matrix_int *patterns, gsl_matrix *probs, gsl_vector *quad_weights, gsl_matrix *post)
	Compute the posteriori probabilities.
void	posteriors_mc (gsl_matrix_int *patterns, gsl_matrix *probs, gsl_vector_int *nbr_options, gsl_vector_int *items_pos, gsl_vector *quad_weights, gsl_matrix *post)
	Compute the posteriori probabilities for multiple choice patterns.
void	frequencies (gsl_matrix_int *patterns, gsl_vector *counts, gsl_matrix *post, gsl_matrix *probs, gsl_vector *quad_sizes, gsl_matrix *quad_freqs)
	Compute the expected numbers of subjects.
int	set_ignore (gsl_matrix_int *patterns, gsl_matrix *probs, gsl_vector *thresholds, gsl_vector_int *ignore)
	Check for degenerate items.
void	constrain_probs (gsl_matrix *probs, double eps)
	Reset the probabilities to be inside the open interval (0,1).
void	patterns_expand (gsl_matrix_int *patterns_mc, gsl_vector_int *items_nbr, gsl_matrix_int *patterns, gsl_vector_int *items_pos)
	Transform a matrix with multiple choice items into a matrix with binary items by creating a new "item"for each option.
int	mle_abilities_3plm (int max_iter, double prec, gsl_matrix_int *patterns, gsl_vector *slopes, gsl_vector *thresholds, gsl_vector *asymptotes, gsl_vector *abilities, gsl_vector *abilities_stddev)
	Estimate the abilities by maximum likelihood.
void	eap_abilities (gsl_matrix *post, gsl_vector *quad_points, gsl_vector *quad_weights, gsl_vector *abilities, gsl_vector *abilities_stddev)
	Estimate the abilities by Bayes exact a posteriori.
int	em_bme_3plm (int nbr_par, int max_em_iter, int max_nr_iter, double prec, gsl_matrix_int *patterns, gsl_vector *counts, gsl_vector *quad_points, gsl_vector *quad_weights, int slope_prior, double slope_mean, double slope_dev, int thresh_prior, double thresh_mean, double thresh_dev, int asymp_prior, double asymp_mean, double asymp_weight, gsl_vector *slopes, gsl_vector *thresholds, gsl_vector *asymptotes, gsl_vector *slopes_stddev, gsl_vector *thresh_stddev, gsl_vector *asymp_stddev, gsl_vector_int *ignore, int *nbr_notconverge, gsl_vector_int *notconverge, int adjust_weights)
	Estimate the parameters of a 2PLM or 3PLM by MMLE or more generally (if a prior is used) by BME.
int	em_mple_wave (int max_em_iter, int max_nr_iter, double prec, double smooth_factor, gsl_matrix_int *patterns, gsl_vector *counts, gsl_vector *quad_points, gsl_vector *quad_weights, gsl_matrix *probs, gsl_matrix *probs_stddev, gsl_vector_int *ignore, int *nbr_notconverge, gsl_vector_int *notconverge, int adjust_weights)
	Estimate the response functions by PMMLE (Penalized Maximum Marginal Likelihood).
void	nadaraya_watson (double bandwidth, gsl_matrix_int *patterns, gsl_vector *quad_points, gsl_vector *quad_weights, gsl_matrix *probs, gsl_matrix *probs_stddev)
	Estimate the response functions by Nadaraya-Watson kernel smoothing (Testgraf).
void	logits_from_probs (gsl_matrix *probs, gsl_matrix *logits)
	Compute the logit from the options characteristic curves.
void	probs_from_logits (gsl_matrix *logits, gsl_matrix *probs)
	Compute the options characteristic curves from the logits.
int	em_mple_wave_mc (int max_em_iter, int max_nr_iter, double prec, double smooth_factor, gsl_matrix_int *patterns, gsl_vector *counts, gsl_vector *quad_points, gsl_vector *quad_weights, gsl_vector_int *items_pos, gsl_vector_int *items_nbr, gsl_matrix *probs, gsl_matrix *probs_stddev, gsl_vector_int *ignore, int *nbr_notconverge, gsl_vector_int *notconverge, int adjust_weights)
	Estimate the options response functions by PMMLE (Penalized Maximum Marginal Likelihood).
int	set_ignore_mc (gsl_matrix_int *patterns, gsl_vector_int *nbr_options, gsl_vector_int *items_pos, gsl_matrix *probs, gsl_vector *thresholds, gsl_vector_int *ignore)
	Check for degenerate multiple choice items.
void	nadaraya_watson_mc (double bandwidth, gsl_matrix_int *patterns, gsl_vector_int *items_pos, gsl_vector_int *nbr_options, gsl_vector *options_weights, gsl_vector *quad_points, gsl_vector *quad_weights, gsl_matrix *probs, gsl_matrix *probs_stddev)
	Estimate the response functions by Nadaraya-Watson kernel smoothing (Testgraf).
void	probs_2plm_mc (gsl_vector *slopes, gsl_vector *thresholds, gsl_vector_int *nbr_options, gsl_vector_int *items_pos, gsl_vector *quad_points, gsl_matrix *probs)
	Compute the response functions for a multivariate logistic model.
int	mmle_2plm_mc (int max_em_iter, int max_nr_iter, double prec, gsl_matrix_int *patterns, gsl_vector *counts, gsl_vector *quad_points, gsl_vector *quad_weights, gsl_vector_int *items_pos, gsl_vector_int *nbr_options, gsl_vector *thresholds, gsl_vector *thresh_stddev, gsl_vector *slopes, gsl_vector *slopes_stddev, gsl_vector_int *ignore, int *nbr_notconverge, gsl_vector_int *notconverge, int adjust_weights)
	Estimate the options response functions by MMLE (Maximum Marginal Likelihood).
void	probs_2plm_grad (gsl_vector *slopes, gsl_vector *thresholds, gsl_vector_int *nbr_options, gsl_vector_int *items_pos, gsl_vector *quad_points, gsl_matrix *probs, gsl_matrix *bounds)
	Compute the response functions for a graded model.
int	mmle_2plm_grad (int max_em_iter, int max_nr_iter, double prec, gsl_matrix_int *patterns, gsl_vector *counts, gsl_vector *quad_points, gsl_vector *quad_weights, gsl_vector_int *items_pos, gsl_vector_int *nbr_options, gsl_vector *thresholds, gsl_vector *thresh_stddev, gsl_vector *slopes, gsl_vector *slopes_stddev, gsl_vector_int *ignore, int *nbr_notconverge, gsl_vector_int *notconverge, int adjust_weights)
	Estimate the options response functions by MMLE (Maximum Marginal Likelihood).
void	icc_from_probs (gsl_matrix *probs, gsl_matrix *probs_stddev, gsl_vector *options_weights, gsl_vector_int *nbr_options, gsl_vector_int *items_pos, gsl_matrix *iccs, gsl_matrix *iccs_stddev)
	Compute the items' characteristic curves from the options' characteristic curves.
void	info_from_probs (gsl_matrix *probs, gsl_vector *quad_points, gsl_matrix *infos, gsl_vector *test_info)
	Compute the items' information curves from the response functions.
void	info_from_probs_mc (gsl_matrix *probs, gsl_vector *quad_points, gsl_vector_int *nbr_options, gsl_vector_int *items_pos, gsl_matrix *options_infos, gsl_matrix *infos, gsl_vector *test_info)
	Compute the options' information curves from the response functions for a multivariate model.
void	llk_ratio_fit_test (gsl_vector *quad_sizes, gsl_matrix *quad_freqs, gsl_vector *quad_weights, gsl_matrix *probs, int nbr_inter, gsl_vector *chi2, gsl_vector_int *df, gsl_vector *p_value)
	Compute the log likelihood ratio statistics of each items.
void	llk_ratio_fit_test_mc (gsl_vector *quad_sizes, gsl_matrix *quad_freqs, gsl_vector *quad_weights, gsl_matrix *probs, gsl_vector_int *nbr_options, gsl_vector_int *items_pos, int nbr_inter, gsl_vector *chi2, gsl_vector_int *df, gsl_vector *p_value)
	Compute the log likelihood ratio statistics of each multiple choice items.
void	classical_statistics (gsl_matrix_int *patterns, gsl_vector *items_mean, gsl_vector *items_sd, gsl_vector *items_corr, gsl_vector *items_bis_corr, gsl_vector_int *items_nbr, gsl_vector *subjects_mean, gsl_vector_int *subjects_nbr, int *nbr, double *mean, double *sd, double *alpha, gsl_matrix *pairs_corr)
	Compute the classical test theory statistics.
void	classical_statistics_mc (gsl_matrix_int *patterns, gsl_vector *options_weights, gsl_vector_int *items_pos, gsl_vector_int *nbr_options, gsl_vector *items_mean, gsl_vector *items_sd, gsl_vector *items_corr, gsl_vector *items_poly_corr, gsl_vector_int *items_nbr, gsl_vector *subjects_score, gsl_vector_int *subjects_nbr, int *nbr, double *mean, double *sd, double *alpha, gsl_matrix *pairs_corr)
	Compute the classical test theory statistics.
void	llk_ratio_ld_test (gsl_matrix_int *patterns, gsl_matrix *probs, gsl_vector *quad_weights, gsl_matrix *chi2, gsl_matrix_int *df, gsl_matrix *p_value)
	Compute the log likelihood ratio statistics of each items pairs for local dependance.
void	llk_ratio_ld_test_mc (gsl_matrix_int *patterns, gsl_matrix *probs, gsl_vector *quad_weights, gsl_vector_int *nbr_options, gsl_vector_int *items_pos, gsl_matrix *chi2, gsl_matrix_int *df, gsl_matrix *p_value)
	Compute the log likelihood ratio statistics of each multiple choice items pairs for local dependance.
void	adjust_quad_weights (double nbr_subject, gsl_vector *quad_sizes, gsl_vector *quad_points, gsl_vector *quad_weights)
	Recompute the quadrature weights based on the observations.
int	wmle_abilities (int max_iter, double prec, gsl_matrix *like, gsl_vector *info, gsl_vector *quad_points, gsl_vector *abilities, gsl_vector *abilities_stddev)
	Compute the WMLE of the abilities.
double	polyserial_factor (gsl_vector_int *patterns, int nbr_option, int offset, gsl_vector *options_weights)
	Compute the polyserial correlation factor to be multiplied to the point-biserial (pearson) correlation.

Variables
const char *	libirt_version
	The version of the library.
int	libirt_verbose
	Control the verbosity level.

Detailed Description

The exported functions definition of the libirt library.

Author

Stephane Germain germs.nosp@m.te@g.nosp@m.mail..nosp@m.com

Macro Definition Documentation

#define LIBIRT_H   1

Define a flag if this header file is already included.

#define BLANK   -1

Define the representation of blank as integer.

#define FALSE   0

Define the representation of false as integer.

#define TRUE   1

Define the representation of true as integer.

#define VERY_SMALL_PROB   ((double)1.0e-10)

Define the smallest probability allowed.

#define VERY_SMALL_FREQ   ((double)1.0e-3)

Define the smallest frequency allowed.

#define VERY_BIG_LOGIT   ((double)23.0)

Define the biggest logit allowed in absolute value.

#define MAX_POLYCOR   ((double)0.9999)

Define the biggest absolute polyserial correlation allowed.

Function Documentation

int read_bin_patterns_delimited	(	FILE *	file,
		int	nbr_item,
		int	nbr_subject,
		int	skip,
		char	delimiter,
		int	offset,
		int	extra,
		char *	true_string,
		char *	false_string,
		char *	blank_string,
		int	trimming,
		gsl_matrix_int **	patterns
	)

Read binary patterns from a file in delimited format.

Parameters

[in]	file	A open file descriptor with a rewind capability (not stdin).
[in]	nbr_item	The number of item to read or 0 for autodetection.
[in]	nbr_subject	The number of pattern to read or 0 for autodetection.
[in]	skip	The number of line to skip at the start of the file.
[in]	delimiter	The delimiter to use.
[in]	offset	The number of field to skip at the start of each line.
[in]	extra	The number of field between the items.
[in]	true_string	The string representing a success.
[in]	false_string	The string representing a failure. If NULL then anything not a success nor a non response will be assume to be a failure.
[in]	blank_string	The string representing a non response. If NULL then anything not a success nor a failure will be assume to be a non response. A empty field is always assumed to be a non response.
[in]	trimming	Enable the trimming of spaces.
[out]	patterns	A matrix(patterns x items) of binary responses.

Returns

1 for success and 0 for failure.

Warning

This function allocate the memory for patterns.

int read_mc_patterns_delimited	(	FILE *	file,
		int	nbr_item,
		int	nbr_subject,
		int	skip,
		char	delimiter,
		int	offset,
		int	extra,
		int	trimming,
		gsl_matrix_int **	patterns,
		gsl_vector_int **	nbr_options
	)

Read multiple choice patterns from a file in delimited format.

The responses are assumed to be positive integer, anything else will be assumed to be a non response.

Parameters

[in]	file	A open file descriptor with a rewind capability (not stdin).
[in]	nbr_item	The number of item to read or 0 for autodetection.
[in]	nbr_subject	The number of pattern to read or 0 for autodetection.
[in]	skip	The number of line to skip at the start of the file.
[in]	delimiter	The delimiter to use.
[in]	offset	The number of field to skip at the start of each line.
[in]	extra	The number of field to ignore after each items.
[in]	trimming	Enable the trimming of spaces.
[out]	patterns	A matrix(patterns x items) of mc responses.
[out]	nbr_options	A vector(items) with the number of option of each item in patterns (and probs).

Returns

1 for success and 0 for failure.

Warning

This function allocate the memory for patterns and nbr_options.

double logit

(

double

p

)

Compute the logit transformation.

Returns

The logit of p.

double logistic

(

double

t

)

Compute the logistic transformation.

Returns

The logistic of t.

double prob_3plm	(	double	ability,
		double	slope,
		double	threshold,
		double	asymptote
	)

Compute the 3 parameter logistic function.

Parameters

[in]	ability
[in]	slope
[in]	threshold
[in]	asymptote

Returns

The 3PLM evaluated at ability.

void quadrature	(	int	nbr_quad,
		double	from,
		double	to,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights
	)

Generate the quadrature classes.

Parameters

[in]	nbr_quad	The number of classes.
[in]	from	The starting value for the middle points of the classes.
[in]	to	The ending value for the middle points of the classes.
[out]	quad_points	A vector(classes) with the middle points of each class.
[out]	quad_weights	A vector(classes) with the normal weights of each class.

void patterns_counts	(	gsl_matrix_int *	subjects,
		gsl_vector_int **	index,
		gsl_matrix_int **	patterns,
		gsl_vector **	counts
	)

Group the identical patterns from subjects into patterns.

Parameters

[in]	subjects	A matrix(subjects x items) of binary responses.
[out]	patterns	A matrix(patterns x items) with the uniques patterns.
[out]	counts	A vector(patterns) with the count of each pattern.
[out]	index	A vector(subjects) with the new position of each subjects in patterns.

Warning

This function allocate the memory for patterns, counts and index

void probs_3plm	(	gsl_vector *	slopes,
		gsl_vector *	thresholds,
		gsl_vector *	asymptotes,
		gsl_vector *	quad_points,
		gsl_matrix *	probs
	)

Compute the response functions for a 3PLM.

Parameters

[in]	slopes	A vector(items) with the slope parameters of each item.
[in]	thresholds	A vector(items) with the threshold parameters of each item.
[in]	asymptotes	A vector(items) with the asymptote parameters of each item. Can be NULL for a 2PLM.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[out]	probs	A matrix(items x classes) with the response functions.

Warning

The memory for probs should be allocated before.

Todo:

Stddev of the probs

void likelihood	(	gsl_matrix_int *	patterns,
		gsl_matrix *	probs,
		gsl_matrix *	like
	)

Compute the likelihood of each patterns.

Parameters

[in]	patterns	A matrix (patterns x items) of binary responses.
[in]	probs	A matrix(items x classes) with response functions.
[out]	like	A matrix(patterns x classes) with the likelihood of each pattern in each quadrature class.

Warning

The memory for likel should be allocated before.

void likelihood_mc	(	gsl_matrix_int *	patterns,
		gsl_matrix *	probs,
		gsl_vector_int *	nbr_options,
		gsl_vector_int *	items_pos,
		gsl_matrix *	like
	)

Compute the likelihood of each multiple choice patterns.

Parameters

[in]	patterns	A matrix (patterns x options) of binary responses.
[in]	probs	A matrix(options x classes) with response functions.
[in]	nbr_options	A vector(items) with the number of option of each items.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns.
[out]	like	A matrix(patterns x classes) with the likelihood of each pattern in each quadrature class.

Warning

The memory for likel should be allocated before.

void posteriors	(	gsl_matrix_int *	patterns,
		gsl_matrix *	probs,
		gsl_vector *	quad_weights,
		gsl_matrix *	post
	)

Compute the posteriori probabilities.

Parameters

[in]	patterns	A matrix (patterns x items) of binary responses.
[in]	probs	A matrix(items x classes) with response functions.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[out]	post	A matrix(patterns x classes) with the probability that a pattern is in a quadrature class.

Warning

The memory for post should be allocated before.

void posteriors_mc	(	gsl_matrix_int *	patterns,
		gsl_matrix *	probs,
		gsl_vector_int *	nbr_options,
		gsl_vector_int *	items_pos,
		gsl_vector *	quad_weights,
		gsl_matrix *	post
	)

Compute the posteriori probabilities for multiple choice patterns.

Parameters

[in]	patterns	A matrix (patterns x options) of binary responses.
[in]	probs	A matrix(options x classes) with response functions.
[in]	nbr_options	A vector(items) with the number of option of each items.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[out]	post	A matrix(patterns x classes) with the probability that a pattern is in a quadrature class.

Warning

The memory for post should be allocated before.

void frequencies	(	gsl_matrix_int *	patterns,
		gsl_vector *	counts,
		gsl_matrix *	post,
		gsl_matrix *	probs,
		gsl_vector *	quad_sizes,
		gsl_matrix *	quad_freqs
	)

Compute the expected numbers of subjects.

Parameters

[in]	patterns	A matrix (patterns x items) of binary responses.
[in]	counts	A vector(patterns) with the count of each pattern.
[in]	post	A matrix(patterns x classes) with the probability that a pattern is in a quadrature class.
[in]	probs	A matrix(items x classes) with response functions. Used to replace the missing data.
[out]	quad_sizes	A vector(classes) with the expected number of subjects in the class.
[out]	quad_freqs	A matrix(items x classes) with the expected number of subjects in the class having a success at the item.

Warning

The memory for quad_sizes and quad_freqs should be allocated before.

Todo:

Recomputing the quad_size for each item is unecessary.

int set_ignore	(	gsl_matrix_int *	patterns,
		gsl_matrix *	probs,
		gsl_vector *	thresholds,
		gsl_vector_int *	ignore
	)

Check for degenerate items.

For each items, check if it's almost either all success or all failures, and if so enable the ignore flag and set the prob accordingly.

Parameters

[in]	patterns	A matrix (patterns x items) of binary responses.
[out]	probs	A matrix (items x classes) of response functions.
[out]	thresholds	A vector(items) with the threshold parameters of each item.
[out]	ignore	A vector (items) of flag.

Returns

The number of items to ignore.

Warning

The memory for the outputs must be allocated before.

void constrain_probs	(	gsl_matrix *	probs,
		double	eps
	)

Reset the probabilities to be inside the open interval (0,1).

Parameters

[in,out]	probs	A matrix (items x classes) of response functions.
[in]	eps	The minimal distance allowed from 0 or 1.

void patterns_expand	(	gsl_matrix_int *	patterns_mc,
		gsl_vector_int *	items_nbr,
		gsl_matrix_int *	patterns,
		gsl_vector_int *	items_pos
	)

Transform a matrix with multiple choice items into a matrix with binary items by creating a new "item"for each option.

Parameters

[in]	patterns_mc	A matrix(patterns x items) of multiple choice responses.
[in]	nbr_options	A vector(items) with the number of option of each items.
[out]	patterns	A matrix(patterns x options) of binary responses.
[out]	items_pos	A vector(items) with the position of the first option of each item in patterns.

Warning

The memory for the outputs must be allocated before.

int mle_abilities_3plm	(	int	max_iter,
		double	prec,
		gsl_matrix_int *	patterns,
		gsl_vector *	slopes,
		gsl_vector *	thresholds,
		gsl_vector *	asymptotes,
		gsl_vector *	abilities,
		gsl_vector *	abilities_stddev
	)

Estimate the abilities by maximum likelihood.

Parameters

[in]	max_iter	The maximum number of Newton iterations performed for each pattern.
[in]	prec	The desired precision of each parameter estimate.
[in]	patterns	A matrix(patterns x items) of binary responses.
[in]	slopes	A vector(items) with the slope parameters of each item.
[in]	thresholds	A vector(items) with the threshold parameters of each item.
[in]	asymptotes	A vector(items) with the asymptote parameters of each item. Can be NULL for the 2PLM.
[in,out]	abilities	A vector(patterns) with the estimated abilities. They should be initialize first.
[out]	abilities_stddev	A vector(items) with the standard errors of the estimated abilities.

Returns

The number of pattern that did not converged.

detect the degenerates patterns.

void eap_abilities	(	gsl_matrix *	post,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights,
		gsl_vector *	abilities,
		gsl_vector *	abilities_stddev
	)

Estimate the abilities by Bayes exact a posteriori.

Work also for expanded multiple choices patterns.

Parameters

[in]	post	A matrix(patterns x classes) with the probability that a pattern is in a quadrature class.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[out]	abilities	A vector(patterns) with the estimated abilities.
[out]	abilities_stddev	A vector(items) with the standard errors of the estimated abilities.

Warning

The memory for abilities and abilities_stddev should be allocated before.

int em_bme_3plm	(	int	nbr_par,
		int	max_em_iter,
		int	max_nr_iter,
		double	prec,
		gsl_matrix_int *	patterns,
		gsl_vector *	counts,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights,
		int	slope_prior,
		double	slope_mean,
		double	slope_dev,
		int	thresh_prior,
		double	thresh_mean,
		double	thresh_dev,
		int	asymp_prior,
		double	asymp_mean,
		double	asymp_weight,
		gsl_vector *	slopes,
		gsl_vector *	thresholds,
		gsl_vector *	asymptotes,
		gsl_vector *	slopes_stddev,
		gsl_vector *	thresh_stddev,
		gsl_vector *	asymp_stddev,
		gsl_vector_int *	ignore,
		int *	nbr_notconverge,
		gsl_vector_int *	notconverge,
		int	adjust_weights
	)

Estimate the parameters of a 2PLM or 3PLM by MMLE or more generally (if a prior is used) by BME.

Parameters

[in]	nbr_par	The number of parameter (1, 2 or 3).
[in]	max_em_iter	The maximum number of EM iterations. At least 20 iteration are made.
[in]	max_nr_iter	The maximum number of Newton iterations performed for each item at each EM iteration.
[in]	prec	The relative change in the likelihood to stop the EM algorithm. This value divided by 10 is also the desired precision of each parameter estimate.
[in]	patterns	A matrix(patterns x items) of binary responses.
[in]	counts	A vector(patterns) with the count of each pattern. If NULL the counts are assumed to be all 1.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[in]	slope_prior	Controls whether to use a lognormal(slope_mean, slope_dev) prior on the slope.
[in]	slope_mean	The mean of the lognormal prior on the slope.
[in]	slope_dev	The standard deviation of the lognormal prior on the slope.
[in]	thresh_prior	Controls whether to use a normal(thresh_mean, thresh_dev) prior on the threshold
[in]	thresh_mean	The mean of the normal prior on the threshold.
[in]	thresh_dev	The standard deviation of the normal prior on the threshold.
[in]	asymp_prior	Controls whether to use a beta(asymp_mean, asymp_weight) prior on the asymptote
[in]	asymp_mean	The mean of the beta prior on the asymptote. The alpha and beta parameter are alpha = mean * weight + 1 and beta = (1 - mean) * weight + 1).
[in]	asymp_weight	The weight of the beta prior on the asymptote. The alpha and beta parameter are alpha = mean * weight + 1 and beta = (1 - mean) * weight + 1).
[in,out]	slopes	A vector(items) with the estimated slope parameters. They should be initialize first.
[out]	slopes_stddev	A vector(items) with the standard errors of the estimated slopes.
[in,out]	thresholds	A vector(items) with the estimated threshold parameters. They should be initialize first.
[out]	thresh_stddev	A vector(items) with the standard errors of the estimated thresholds.
[in,out]	asymptotes	A vector(items) with the estimated asymptote parameters. They should be initialize first.
[out]	asymp_stddev	A vector(items) with the standard errors of the estimated asymptotes.
[in]	ignore	A vector(items) of ignore flag.
[out]	nbr_notconverge	The number of items that didn't converged.
[out]	notconverge	A vector(items) of flag set for the items that didn't converged.
[in]	adjust_weights	Controls whether adjust the quadrature weights after each iteration.

Returns

1 if the relative change in the maximum log likelihood was less than prec else 0.

Warning

The memory for the output parameters should be allocated before.

Todo:

Check for the biggest change in the EM iterations and add a stop criterion.

int em_mple_wave	(	int	max_em_iter,
		int	max_nr_iter,
		double	prec,
		double	smooth_factor,
		gsl_matrix_int *	patterns,
		gsl_vector *	counts,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights,
		gsl_matrix *	probs,
		gsl_matrix *	probs_stddev,
		gsl_vector_int *	ignore,
		int *	nbr_notconverge,
		gsl_vector_int *	notconverge,
		int	adjust_weights
	)

Estimate the response functions by PMMLE (Penalized Maximum Marginal Likelihood).

Parameters

[in]	max_em_iter	The maximum number of EM iterations. At least 20 iteration are made.
[in]	max_nr_iter	The maximum number of Newton iterations performed for each item at each EM iteration.
[in]	prec	The relative change in the likelihood to stop the EM algorithm. This value divided by 10 is also the desired precision of each parameter estimate.
[in]	smooth_factor	The factor to the penality term.
[in]	patterns	A matrix(patterns x items) of binary responses.
[in]	counts	A vector(patterns) with the count of each pattern. If NULL the counts are assumed to be all 1.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[in,out]	probs	A matrix(items x classes) with the estimated response functions. They should be initialize first.
[out]	probs_stddev	matrix(items x classes) with the standard error of the logit response functions.
[in]	ignore	A vector(items) of ignore flag.
[out]	nbr_notconverge	The number of items that didn't converged.
[out]	notconverge	A vector(items) of flag set for the items that didn't converged.
[in]	adjust_weights	Controls whether adjust the quadrature weights after each iteration.

Returns

The number of item that did not converged at the last EM iteration.

Warning

The memory for the response functions should be allocated before.

Todo:

Compute more accurates wavelets derivatives

void nadaraya_watson	(	double	bandwidth,
		gsl_matrix_int *	patterns,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights,
		gsl_matrix *	probs,
		gsl_matrix *	probs_stddev
	)

Estimate the response functions by Nadaraya-Watson kernel smoothing (Testgraf).

Parameters

[in]	bandwidth	The smoothing parameter, will be multiply by the number of distinct scores to the power of -0.2 to give the bandwidth.
[in]	patterns	A matrix(patterns x items).
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[out]	probs	A matrix(items x classes) with the estimated response functions. They should be initialize first.
[out]	probs_stddev	matrix(items x classes) with the standard error of the logit response functions.

Warning

Do not group the patterns before.

The memory for the response functions should be allocated before.

void logits_from_probs	(	gsl_matrix *	probs,
		gsl_matrix *	logits
	)

Compute the logit from the options characteristic curves.

Parameters

[in]	probs	A matrix(options x classes).
[out]	logits	A matrix(logits x classes).

void probs_from_logits	(	gsl_matrix *	logits,
		gsl_matrix *	probs
	)

Compute the options characteristic curves from the logits.

Parameters

[in]	logits	A matrix(logits x classes).
[out]	probs	A matrix(options x classes).

int em_mple_wave_mc	(	int	max_em_iter,
		int	max_nr_iter,
		double	prec,
		double	smooth_factor,
		gsl_matrix_int *	patterns,
		gsl_vector *	counts,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights,
		gsl_vector_int *	items_pos,
		gsl_vector_int *	nbr_options,
		gsl_matrix *	probs,
		gsl_matrix *	probs_stddev,
		gsl_vector_int *	ignore,
		int *	nbr_notconverge,
		gsl_vector_int *	notconverge,
		int	adjust_weights
	)

Estimate the options response functions by PMMLE (Penalized Maximum Marginal Likelihood).

Parameters

[in]	max_em_iter	The maximum number of EM iterations. At least 20 iteration are made.
[in]	max_nr_iter	The maximum number of Newton iterations performed for each item at each EM iteration.
[in]	prec	The relative change in the likelihood to stop the EM algorithm. This value divided by 10 is also the desired precision of each parameter estimate.
[in]	smooth_factor	The factor to the penality term.
[in]	patterns	A matrix(patterns x options) of binary responses.
[in]	counts	A vector(patterns) with the count of each pattern. If NULL the counts are assumed to be all 1.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns (and probs).
[in]	nbr_options	A vector(items) with the number of option of each item in patterns (and probs).
[in,out]	probs	A matrix(options x classes) with the estimated response functions. They should be initialize first.
[out]	probs_stddev	matrix(items x classes) with the standard error of the logit response functions.
[in]	ignore	A vector(items) of ignore flag.
[out]	nbr_notconverge	The number of items that didn't converged.
[out]	notconverge	A vector(items) of flag set for the items that didn't converged.
[in]	adjust_weights	Controls whether adjust the quadrature weights after each iteration.

Returns

1 if the relative change in the maximum log likelihood was less than prec else 0.

Warning

The memory for the outputs should be allocated before.

Todo:

Compute more accurates wavelets derivatives

int set_ignore_mc	(	gsl_matrix_int *	patterns,
		gsl_vector_int *	nbr_options,
		gsl_vector_int *	items_pos,
		gsl_matrix *	probs,
		gsl_vector *	thresholds,
		gsl_vector_int *	ignore
	)

Check for degenerate multiple choice items.

For each items, check if a option is all success, and if so enable the ignore flag and set the prob accordingly.

Parameters

[in]	patterns	A matrix (patterns x options) of binary responses.
[in]	nbr_options	A vector(items) with the number of option of each items.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns.
[out]	probs	A matrix (options x classes) of option response functions.
[out]	thresholds	A vector(options) with the threshold parameters of each logit.
[out]	ignore	A vector (items) of flag.

Returns

The number of items to ignore.

Warning

The memory for the outputs must be allocated before.

void nadaraya_watson_mc	(	double	bandwidth,
		gsl_matrix_int *	patterns,
		gsl_vector_int *	items_pos,
		gsl_vector_int *	nbr_options,
		gsl_vector *	options_weights,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights,
		gsl_matrix *	probs,
		gsl_matrix *	probs_stddev
	)

Estimate the response functions by Nadaraya-Watson kernel smoothing (Testgraf).

Parameters

[in]	bandwidth	The smoothing parameter, will be multiply by the number of distinct scores to the power of -0.2 to give the bandwidth.
[in]	patterns	A matrix(patterns x options) of binary response.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns (and probs).
[in]	nbr_options	A vector(items) with the number of option of each item in patterns (and probs).
[in]	options_weights	A vector(options) of weights to compute the score.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[out]	probs	A matrix(options x classes) with the estimated response functions.
[out]	probs_stddev	matrix(options x classes) with the standard error.

Warning

Do not group the patterns before.

The memory for the response functions should be allocated before.

void probs_2plm_mc	(	gsl_vector *	slopes,
		gsl_vector *	thresholds,
		gsl_vector_int *	nbr_options,
		gsl_vector_int *	items_pos,
		gsl_vector *	quad_points,
		gsl_matrix *	probs
	)

Compute the response functions for a multivariate logistic model.

Parameters

[in]	slopes	A vector(options) with the slope parameters of each option.
[in]	thresholds	A vector(options) with the threshold parameters of each option.
[in]	nbr_options	A vector(items) with the number of option of each items.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[out]	probs	A matrix(options x classes) with the response functions.

Todo:

Stddev of the probs

Warning

The memory for probs should be allocated before.

int mmle_2plm_mc	(	int	max_em_iter,
		int	max_nr_iter,
		double	prec,
		gsl_matrix_int *	patterns,
		gsl_vector *	counts,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights,
		gsl_vector_int *	items_pos,
		gsl_vector_int *	nbr_options,
		gsl_vector *	thresholds,
		gsl_vector *	thresh_stddev,
		gsl_vector *	slopes,
		gsl_vector *	slopes_stddev,
		gsl_vector_int *	ignore,
		int *	nbr_notconverge,
		gsl_vector_int *	notconverge,
		int	adjust_weights
	)

Estimate the options response functions by MMLE (Maximum Marginal Likelihood).

Parameters

[in]	max_em_iter	The maximum number of EM iterations. At least 20 iteration are made.
[in]	max_nr_iter	The maximum number of Newton iterations performed for each item at each EM iteration.
[in]	prec	The relative change in the likelihood to stop the EM algorithm. This value divided by 10 is also the desired precision of each parameter estimate.
[in]	patterns	A matrix(patterns x options) of binary responses.
[in]	counts	A vector(patterns) with the count of each pattern. If NULL the counts are assumed to be all 1.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns (and probs).
[in]	nbr_options	A vector(items) with the number of option of each item in patterns (and probs).
[in,out]	thresholds	A vector(options) with the estimated thresholds. They should be initialize first.
[out]	thresh_stddev	A vector(options) with the estimated thresholds standard deviation.
[in,out]	slopes	A vector(options) with the estimated slopes. They should be initialize first.
[out]	slopes_stddev	A vector(options) with the estimated slopes standard deviation.
[in]	ignore	A vector(items) of ignore flag.
[out]	nbr_notconverge	The number of items that didn't converged.
[out]	notconverge	A vector(items) of flag set for the items that didn't converged.
[in]	adjust_weights	Controls whether adjust the quadrature weights after each iteration.

Returns

1 if the relative change in the maximum log likelihood was less than prec else 0.

Warning

The memory for the outputs should be allocated before.

void probs_2plm_grad	(	gsl_vector *	slopes,
		gsl_vector *	thresholds,
		gsl_vector_int *	nbr_options,
		gsl_vector_int *	items_pos,
		gsl_vector *	quad_points,
		gsl_matrix *	probs,
		gsl_matrix *	bounds
	)

Compute the response functions for a graded model.

Parameters

[in]	slopes	A vector(items) with the slope parameters of each item.
[in]	thresholds	A vector(options) with the "modal" threshold parameters of each option.
[in]	nbr_options	A vector(items) with the number of option of each items. Optional, assumed there is only one item.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns. Optional, assumed threre is only one item.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[out]	probs	A matrix(options x classes) with the response functions.
[out]	bounds	A matrix((options+items) x classes) with the boundary functions including the 0-th and last. Optional.

Todo:

Stddev of the probs

Warning

The memory for probs and bounds should be allocated before.

int mmle_2plm_grad	(	int	max_em_iter,
		int	max_nr_iter,
		double	prec,
		gsl_matrix_int *	patterns,
		gsl_vector *	counts,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights,
		gsl_vector_int *	items_pos,
		gsl_vector_int *	nbr_options,
		gsl_vector *	thresholds,
		gsl_vector *	thresh_stddev,
		gsl_vector *	slopes,
		gsl_vector *	slopes_stddev,
		gsl_vector_int *	ignore,
		int *	nbr_notconverge,
		gsl_vector_int *	notconverge,
		int	adjust_weights
	)

Estimate the options response functions by MMLE (Maximum Marginal Likelihood).

Parameters

[in]	max_em_iter	The maximum number of EM iterations. At least 20 iteration are made.
[in]	max_nr_iter	The maximum number of Newton iterations performed for each item at each EM iteration.
[in]	prec	The relative change in the likelihood to stop the EM algorithm. This value divided by 10 is also the desired precision of each parameter estimate.
[in]	patterns	A matrix(patterns x options) of binary responses.
[in]	counts	A vector(patterns) with the count of each pattern. If NULL the counts are assumed to be all 1.
[in]	quad_points	A vector(classes) with the middle points of each quadrature class.
[in]	quad_weights	A vector(classes) with the prior weights of each quadrature class.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns (and probs).
[in]	nbr_options	A vector(items) with the number of option of each item in patterns (and probs).
[in,out]	thresholds	A vector(options) with the estimated "modal" thresholds. They should be initialize first.
[out]	thresh_stddev	A vector(options) with the estimated thresholds standard deviation.
[in,out]	slopes	A vector(items) with the estimated slopes. They should be initialize first.
[out]	slopes_stddev	A vector(items) with the estimated slopes standard deviation.
[in]	ignore	A vector(items) of ignore flag.
[out]	nbr_notconverge	The number of items that didn't converged.
[out]	notconverge	A vector(items) of flag set for the items that didn't converged.
[in]	adjust_weights	Controls whether adjust the quadrature weights after each iteration.

Returns

1 if the relative change in the maximum log likelihood was less than prec else 0.

Warning

The memory for the outputs should be allocated before.

void icc_from_probs	(	gsl_matrix *	probs,
		gsl_matrix *	probs_stddev,
		gsl_vector *	options_weights,
		gsl_vector_int *	nbr_options,
		gsl_vector_int *	items_pos,
		gsl_matrix *	iccs,
		gsl_matrix *	iccs_stddev
	)

Compute the items' characteristic curves from the options' characteristic curves.

Parameters

[in]	probs	A matrix (options x classes) of options' characteristic curves.
[in]	probs_stddev	A matrix (options x classes) of occ standard error.
[in]	options_weights	A vector (options) of options' weights.
[in]	nbr_options	A vector(items) with the number of option of each items.
[in]	items_pos	A vector(items) with the position of the first option of each item.
[out]	iccs	A matrix (items+1 x classes) of items' characteristic curves and the test characteristic curve.
[out]	iccs_stddev	A matrix (items+1 x classes) of icc standard error.

Warning

The memory for the outputs must be allocated before.

void info_from_probs	(	gsl_matrix *	probs,
		gsl_vector *	quad_points,
		gsl_matrix *	infos,
		gsl_vector *	test_info
	)

Compute the items' information curves from the response functions.

Parameters

[in]	probs	A matrix (items x classes) of response functions.
[in]	quad_points	A vector(classes) with the middle points of each class.
[out]	infos	A matrix (items x classes) of items' information curves.
[out]	test_info	A vector (classes) with test information curve.

Warning

The memory for the outputs must be allocated before.

void info_from_probs_mc	(	gsl_matrix *	probs,
		gsl_vector *	quad_points,
		gsl_vector_int *	nbr_options,
		gsl_vector_int *	items_pos,
		gsl_matrix *	options_infos,
		gsl_matrix *	infos,
		gsl_vector *	test_info
	)

Compute the options' information curves from the response functions for a multivariate model.

Parameters

[in]	probs	A matrix (options x classes) of response functions.
[in]	quad_points	A vector(classes) with the middle points of each class.
[in]	nbr_options	A vector(items) with the number of option of each items.
[in]	items_pos	A vector(items) with the position of the first option of each item.
[out]	options_infos	A matrix (options x classes) of options' information curves.
[out]	infos	A matrix (items x classes) of items' information curves.
[out]	test_info	A vector (classes) with test information curve.

Warning

The memory for the outputs must be allocated before.

void llk_ratio_fit_test	(	gsl_vector *	quad_sizes,
		gsl_matrix *	quad_freqs,
		gsl_vector *	quad_weights,
		gsl_matrix *	probs,
		int	nbr_inter,
		gsl_vector *	chi2,
		gsl_vector_int *	df,
		gsl_vector *	p_value
	)

Compute the log likelihood ratio statistics of each items.

Parameters

[in]	quad_sizes	A vector(classes) with the expected number of subjects in each class.
[in]	quad_freqs	A matrix(items x classes) with the expected number of subjects in the class having a success at the item.
[in]	quad_weights	A vector(classes) with the normal weights of each class.
[in]	probs	A matrix(items x classes) with response functions.
[in]	nbr_inter	The number of intervals to use.
[out]	chi2	A vector(items+1) with the statistics of each items and for the overall fit.
[out]	df	A vector(items+1) with the degrees of freedom.
[out]	p_value	A vector(items+1) with the p-values.

Warning

The memory for the outputs should be allocated before.

void llk_ratio_fit_test_mc	(	gsl_vector *	quad_sizes,
		gsl_matrix *	quad_freqs,
		gsl_vector *	quad_weights,
		gsl_matrix *	probs,
		gsl_vector_int *	nbr_options,
		gsl_vector_int *	items_pos,
		int	nbr_inter,
		gsl_vector *	chi2,
		gsl_vector_int *	df,
		gsl_vector *	p_value
	)

Compute the log likelihood ratio statistics of each multiple choice items.

Parameters

[in]	quad_sizes	A vector(classes) with the expected number of subjects in each class.
[in]	quad_freqs	A matrix(options x classes) with the expected number of subjects in the class having a success at the option.
[in]	quad_weights	A vector(classes) with the normal weights of each class.
[in]	probs	A matrix(options x classes) with response functions.
[in]	nbr_options	A vector(items) with the number of option of each items.
[in]	items_pos	A vector(items) with the position of the first option of each item.
[in]	nbr_inter	The number of intervals to use.
[out]	chi2	A vector(items+1) with the statistics of each items and for the overall fit.
[out]	df	A vector(items+1) with the degrees of freedom.
[out]	p_value	A vector(items+1) with the p-values.

Warning

The memory for the outputs should be allocated before.

void classical_statistics	(	gsl_matrix_int *	patterns,
		gsl_vector *	items_mean,
		gsl_vector *	items_sd,
		gsl_vector *	items_corr,
		gsl_vector *	items_bis_corr,
		gsl_vector_int *	items_nbr,
		gsl_vector *	subjects_score,
		gsl_vector_int *	subjects_nbr,
		int *	nbr,
		double *	mean,
		double *	sd,
		double *	alpha,
		gsl_matrix *	pairs_corr
	)

Compute the classical test theory statistics.

Parameters

[in]	patterns	A matrix(subjects x items) with the binary patterns.
[out]	items_mean	A vector(items) with the means of each items.
[out]	items_sd	A vector(items) with the sd of each items.
[out]	items_corr	A vector(items) with the correlations between each items and the score of each subject without the item.
[out]	items_bis_corr	A vector(items) with the biserial correlations between each items and the score of each subject without the item.
[out]	items_nbr	A vector(items) with the number of non missing response for each items.
[out]	subjects_score	A vector(subjects) with the scores of each subjects.
[out]	subjects_nbr	A vector(subjects) with the number of non missing response of each subjects.
[out]	nbr	The total number of non missing response.
[out]	mean	The mean score.
[out]	sd	The score sd.
[out]	alpha	The fiability coefficient alpha.
[out]	pairs_corr	A matrix(items x items) of correlation for each pair of items

Warning

The memory for the outputs should be allocated before.

void classical_statistics_mc	(	gsl_matrix_int *	patterns,
		gsl_vector *	options_weights,
		gsl_vector_int *	items_pos,
		gsl_vector_int *	nbr_options,
		gsl_vector *	items_mean,
		gsl_vector *	items_sd,
		gsl_vector *	items_corr,
		gsl_vector *	items_poly_corr,
		gsl_vector_int *	items_nbr,
		gsl_vector *	subjects_score,
		gsl_vector_int *	subjects_nbr,
		int *	nbr,
		double *	mean,
		double *	sd,
		double *	alpha,
		gsl_matrix *	pairs_corr
	)

Compute the classical test theory statistics.

Parameters

[in]	patterns	A matrix(subjects x items) with the multiple choice patterns.
[in]	options_weights	A vector(options) of weights to compute the score.
[in]	items_pos	A vector(items) with the position of the first option of each item in patterns (and probs).
[in]	nbr_options	A vector(items) with the number of option of each item in patterns (and probs).
[out]	items_mean	A vector(items) with the means of each items.
[out]	items_sd	A vector(items) with the sd of each items.
[out]	items_corr	A vector(items) with the correlations between each items and the score of each subject without the item.
[out]	items_poly_corr	A vector(items) with the polyserial correlations between each items and the score of each subject without the item.
[out]	items_nbr	A vector(items) with the number of non missing response for each items.
[out]	subjects_score	A vector(subjects) with the scores of each subjects.
[out]	subjects_nbr	A vector(subjects) with the number of non missing response of each subjects.
[out]	nbr	The total number of non missing response.
[out]	mean	The mean score.
[out]	sd	The score sd.
[out]	alpha	The fiability coefficient alpha.
[out]	pairs_corr	A matrix(items x items) of correlation for each pair of items

Warning

The memory for the outputs should be allocated before.

void llk_ratio_ld_test	(	gsl_matrix_int *	patterns,
		gsl_matrix *	probs,
		gsl_vector *	quad_weights,
		gsl_matrix *	chi2,
		gsl_matrix_int *	df,
		gsl_matrix *	p_value
	)

Compute the log likelihood ratio statistics of each items pairs for local dependance.

Parameters

[in]	patterns	A matrix(subjects x items) with binary response.
[in]	probs	A matrix(items x classes) with response functions.
[in]	quad_weights	A vector(classes) with the normal weights of each class.
[out]	chi2	A matrix(items x items) with the statistics of each items pairs.
[out]	df	A vector(items x items) with the degrees of freedom.
[out]	p_value	A matrix(items x items) with the p-values of each items pairs.

Warning

The memory for the outputs should be allocated before.

void llk_ratio_ld_test_mc	(	gsl_matrix_int *	patterns,
		gsl_matrix *	probs,
		gsl_vector *	quad_weights,
		gsl_vector_int *	nbr_options,
		gsl_vector_int *	items_pos,
		gsl_matrix *	chi2,
		gsl_matrix_int *	df,
		gsl_matrix *	p_value
	)

Compute the log likelihood ratio statistics of each multiple choice items pairs for local dependance.

Parameters

[in]	patterns	A matrix(subjects x items) with the responses.
[in]	probs	A matrix(options x classes) with response functions.
[in]	nbr_options	A vector(items) with the number of option of each items.
[in]	items_pos	A vector(items) with the position of the first option of each item.
[in]	quad_weights	A vector(classes) with the normal weights of each class.
[out]	chi2	A matrix(items x items) with the statistics of each items pairs.
[out]	df	A vector(items x items) with the degrees of freedom.
[out]	p_value	A matrix(items x items) with the p-values of each items pairs.

Warning

The memory for the outputs should be allocated before.

void adjust_quad_weights	(	double	nbr_subject,
		gsl_vector *	quad_sizes,
		gsl_vector *	quad_points,
		gsl_vector *	quad_weights
	)

Recompute the quadrature weights based on the observations.

Parameters

[in]	nbr_subject	the number of subjects.
[in]	quad_sizes	A vector(classes) with the expected number of subjects in the class.
[in,out]	quad_points	A vector(classes) with the middle points of each class.
[out]	quad_weights	A vector(classes) with the prior weights of each quadrature class.

Warning

The memory for quad_weights should be allocated before.

int wmle_abilities	(	int	max_iter,
		double	prec,
		gsl_matrix *	like,
		gsl_vector *	info,
		gsl_vector *	quad_points,
		gsl_vector *	abilities,
		gsl_vector *	abilities_stddev
	)

Compute the WMLE of the abilities.

Parameters

[in]	max_iter	The maximum number of Newton iterations performed for each pattern.
[in]	prec	The desired precision of each parameter estimate.
[in]	like	A matrix (patterns x classes) of likelihood functions.
[in]	info	A vecor (classes) with the test information function.
[in]	quad_points	A vector(classes) with the middle points of each class.
[out]	abilities	A vector(patterns) with the estimated abilities.
[out]	abilities_stddev	A vector(items) with the standard errors of the estimated abilities.

Warning

The memory for abilities and abilities_stddev should be allocated before.

double polyserial_factor	(	gsl_vector_int *	patterns,
		int	nbr_option,
		int	offset,
		gsl_vector *	options_weights
	)

Compute the polyserial correlation factor to be multiplied to the point-biserial (pearson) correlation.

Parameters

[in]	patterns	A vector(subjects) with the responses.
[in]	nbr_option	The number of option..
[in]	offset	The value of the forst option.
[in]	options_weights	The weights of each option.

If there is no weights or the weights are not strictly increasing or there is only two options, then the biserial correlation factor is calculated (i.e. the response are corrected with the option having the biggest weight.

Returns

The polyserial correlation factor.

Variable Documentation

const char* libirt_version

The version of the library.

int libirt_verbose

Control the verbosity level.

By default it is 0 (silent).